Finite Group Databasebeta

← C₅×C₁₁×C₉₇⋊C₃ #30630754

Subgroups — C₅×C₁₁×C₉₇⋊C₃ #30630754

Order 16005.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₉₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₉₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×C₉₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₉₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₉₇⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₁₁	—	97	1	no	maximal, Hall
8	C₉₇	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₁	C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₁	—	97	1	no	Hall
11	C₃×C₅	—	97	1	no	Hall
12	C₁₁	C₅×C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₅	C₁₁×C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	97	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁	C₉₇⋊C₃
commutator, cosocle, hypocenter	C₉₇	C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₉₇	C₃
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₅×C₁₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×C₁₁×C₉₇	C₃	semidirect
2. C₁₁×C₉₇⋊C₃	C₅	direct (N × H)
3. C₅×C₉₇⋊C₃	C₁₁	direct (N × H)
4. C₁₁×C₉₇	C₃×C₅	semidirect
5. C₅×C₉₇	C₃×C₁₁	semidirect
6. C₉₇⋊C₃	C₅×C₁₁	direct (N × H)
8. C₉₇	C₃×C₅×C₁₁	semidirect
9. C₅×C₁₁	C₉₇⋊C₃	direct (N × H)
12. C₁₁	C₅×C₉₇⋊C₃	direct (N × H)
13. C₅	C₁₁×C₉₇⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₁₁×C₉₇	3
C₁₁×C₉₇⋊C₃	5
C₅×C₉₇⋊C₃	11
C₃×C₅×C₁₁	97